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Algebra
First Degree Inequality Examples
First Degree Inequality Example 1
Question
Solving the first degree inequality - 7x >= 35
Solution
A first-degree inequality is an inequality of the form ax + b < 0 ; ax + b > 0
or ax + b <= 0 ; ax + b >= 0 , where a, b are constant real numbers with a is not zero and x is a veriable.
( note: ax + b <= 0 means ax + b is less than or equal to 0 )
- 7x >= 35 , both sides divide by 7 ,
obtain -x >= 5 , both sides multiply -1 , obtain x <= -5
Therefore, the solution is x <= -5
Note the multiplication properties for inequalities is:
(i) If a < b and c > 0, then ac < bc
(ii) If a < b and c < 0, then ac > bc
That is, when both sides of an inequality multiply a negative number, the inequality changes direction.
First Degree Inequality Example 2
Question
Solving the first degree inequality 2 ( x + 3 ) < 3 ( x + 1 )
Solution
2 ( x + 3 ) < 3 ( x + 1 )
2x + 6 < 3x + 3
2x - 3x < - 6 + 3
- x < - 3 , both sides multiply -1
x > 3 , therefore, the solution is x > 3
First Degree Inequality Example 3
Question
Solving the first degree inequality 5 < 3x - 7 < 11
Solution
The compound inequality 5 < 3x - 7 < 11 consists of 5 < 3x - 7 and 3x - 7 < 11
Solving the inequalities:
case 1:
5 < 3x - 7
move the variable to the left side of the inequality and move the number to the right side of the inequality
- 3x < - 5 - 7
- 3x < - 12
divide by 3 on both side of the inequality
- x < - 4
multiply (-1) on both side of the inequality
x > 4
note: when both side of the inequality multiply (-1), the inequality change direction.
case 2:
3x - 7 < 11
move the number to the right side of the inequality
3x < 7 + 11
3x < 18
x < 6
therefore, the solution of the given inequality is: 4 < x < 6
The solution of the compound inequalities is: 4 < x < 6